Abstract

The maximum rate of global ecophagy by biovorous self-replicating nanorobots is fundamentally restricted by the replicative strategy employed; by the maximum dispersal velocity of mobile replicators; by operational energy and chemical element requirements; by the homeostatic resistance of biological ecologies to ecophagy; by ecophagic thermal pollution limits (ETPL); and most importantly by our determination and readiness to stop them. Assuming current and foreseeable energy-dissipative designs requiring ~100 MJ/kg for chemical transformations (most likely for biovorous systems), ecophagy that proceeds slowly enough to add ~4°C to global warming (near the current threshold for immediate climatological detection) will require ~20 months to run to completion; faster ecophagic devices run hotter, allowing quicker detection by policing authorities. All ecophagic scenarios examined appear to permit early detection by vigilant monitoring, thus enabling rapid deployment of effective defensive instrumentalities.

1.0 Introduction

Recent discussions [1] of the possible dangers posed by future technologies such as artificial intelligence, genetic engineering and molecular nanotechnology have made it clear that an intensive theoretical analysis of the major classes of environmental risks of molecular nanotechnology (MNT) is warranted. No systematic assessment of the risks and limitations of MNT-based technologies has yet been attempted. This paper represents a first effort to begin this analytical process in a quantitative fashion.

Perhaps the earliest-recognized and best-known danger of molecular nanotechnology is the risk that self-replicating nanorobots capable of functioning autonomously in the natural environment could quickly convert that natural environment (e.g., "biomass") into replicas of themselves (e.g., "nanomass") on a global basis, a scenario usually referred to as the "gray goo problem" but perhaps more properly termed "global ecophagy."

"Plants" with "leaves"
no more efficient than today's solar cells could out-compete real plants,
crowding the biosphere with an inedible foliage. Tough omnivorous "bacteria"
could out-compete real bacteria: They could spread like blowing pollen,
replicate swiftly, and reduce the biosphere to dust in a matter of days.
Dangerous replicators could easily be too tough, small, and rapidly spreading
to stop - at least if we make no preparation. We have trouble enough controlling
viruses and fruit flies.

Among the cognoscenti of
nanotechnology, this threat has become known as the "gray goo problem."
Though masses of uncontrolled replicators need not be gray or gooey, the
term "gray goo" emphasizes that replicators able to obliterate life might
be less inspiring than a single species of crabgrass. They might be superior
in an evolutionary sense, but this need not make them valuable.

Gray goo would surely be
a depressing ending to our human adventure on Earth, far worse than mere
fire or ice, and one that could stem from a simple laboratory accident.

Lederberg [3] notes that the microbial world is evolving at a fast pace, and suggests that our survival may depend upon embracing a "more microbial point of view." The emergence of new infectious agents such as HIV and Ebola demonstrates that we have as yet little knowledge of how natural or technological disruptions to the environment might trigger mutations in known organisms or unknown extant organisms [81], producing a limited form of "green goo" [92].

However, biovorous nanorobots capable of comprehensive ecophagy will not be easy to build and their design will require exquisite attention to numerous complex specifications and operational challenges. Such biovores can emerge only after a lengthy period of purposeful focused effort, or as a result of deliberate experiments aimed at creating general-purpose artificial life, perhaps by employing genetic algorithms, and are highly unlikely to arise solely by accident.

However, atoms of Al, Ti and B are far more abundant in the Earth's
crust (81,300 ppm, 4400 ppm and 3 ppm, respectively [5])
than in biomass, e.g., the human body (0.1 ppm, 0 ppm, and 0.03 ppm [6]),
reducing the direct threat of ecophagy by such systems (Section
8.3). On the other hand, carbon is a thousand times less abundant in
crustal rocks (320 ppm, mostly carbonates) than in the biosphere (~230,000
ppm).

Furthermore, conversion of the lithosphere into nanomachinery is not
a primary concern because ordinary rocks typically contain relatively scarce
sources of energy. For instance, natural radioactive isotopes present in
crustal rocks vary greatly as a function of the geological composition
and history of a region, but generally range from 0.15-1.40 mGy/yr [7],
giving a raw power density of 0.28-2.6 ×10-7
W/m3 assuming crustal rocks of approximately mean terrestrial
density (5522 kg/m3 [5]). This is
quite insufficient to power nanorobots capable of significant activities;
current nanomachine designs typically require power densities on the order
of 105-109 W/m3 to achieve effective results
[6]. (Biological systems typically operate
at 102-106 W/m3 [6].)
Solar power is not readily available below the surface, and the mean geothermal
heat flow is only 0.05 W/m2 at the surface [6],
just a tiny fraction of solar insolation. Subsurface pressure and temperature
rise with depth in Earth's crust at the rates of 0.47 atm/meter and kq
~ 0.014°K/meter [8], exceeding maximum
reasonable nanorobot operating limits of 100,000 atm and 2000°K at
depths of ~210 km and ~120 km well into the upper mantle below a ~50 km
crust; however, geothermal power density is only Dp
~ Ktkq2kCarnot
/
DT ~ 1-4 ×10-6
W/m3 taking thermal conductivity Kt
~ 2-5 W/m-K for common crustal minerals [9]
and DT ~
1°C giving Carnot efficiency kCarnot
= DT / T
~ 0.3% at T = 300°K.

Hypothesized crustal abiotic highly-reduced petroleum reserves [16]
probably could not energize significant replicator nanomass growth due
to the anoxic environment deep underground, although potentially large
geobacterial populations have been described [10-16]
and in principle some unusual though highly limited bacterial energy sources
could also be tapped by nanorobots. For example, some anaerobic bacteria
use metals (instead of oxygen) as electron-acceptors [13],
with iron present in minerals such as pyroxene or olivine being converted
to iron in a more oxidized state in magnetic minerals such as magnetite
and maghemite, and using geochemically produced hydrogen to reduce CO2
to methane [11]. Underground bacteria in the
Antrim Shale deposit produce 1.2 ×107 m3/day
of natural gas (methane) by consuming the 370 MY-old remains of ancient
algae [17]. Bioremediation experiments have
also been done by Envirogen and others in which pollution-eating bacteria
are purposely injected into the ground to metabolize organic toxins; in
field tests it has proven difficult to get the bacteria to move through
underground aquifers, because the negatively-charged cells tend to adhere
to positively charged iron oxides in the soil [18].

However, the primary ecophagic concern is that runaway nanorobotic replicators
or "replibots" will convert the entire surface biosphere (the ecology of
all living things on the surface of the Earth) into alternative or artificial
materials of some type -- especially, materials like themselves, e.g.,
more self-replicating nanorobots. Since advanced nanorobots might be constructed
predominantly of carbon-rich diamondoid materials [4],
and since ~12% of all atoms in the human body (representative of biology
generally) are carbon atoms [6], or ~23% by
weight, the global biological carbon inventory may support the self-manufacture
of a final mass of replicating diamondoid nanorobots on the order of ~0.23
Mbio,
where Mbio is the total
global biomass.

Unlike almost any other natural material, biomass can serve both as
a source of carbon and as a source of power for nanomachine replication.
Ecophagic nanorobots would regard living things as environmental carbon
accumulators, and biomass as a valuable ore to be mined for carbon and
energy. Of course, biosystems from which all carbon has been extracted
can no longer be alive but would instead become lifeless chemical sludge.

3.0 Exponential Replication
Rate

Ignoring thermal pollution considerations for the moment (Section
6.0), in theory an optimally designed and geographically uniformly
distributed population of replibots could increase the mass of their own
population at the expense of the biosphere, via self-replication, according
to the simple relation [19]:

Mrepl = Minite(t/t)

(1)

for maximum exponential growth, where t
is elapsed time (sec), t
is generation cycle or replication time (sec), Minit
(kg) is initial nanorobot mass at time t
= 0, and Mrepl (kg) is the
replicator mass at time t, where Mrepl 0.23 Mbio.
In order to achieve this rate, each completed component of the unit currently
being built must be put to full productive use immediately, instead of
waiting for the final completion of the unit. There are a few design
configurations where something close to this can be achieved efficiently,
but as a practical matter and to retain simplicity it will usually be preferable
to await the completion of a unit before pressing it into replicative service,
a mode of operation called discrete replication, in which case the exponential
term in Eqn. 1 should be replaced with 2(t/tdiscrete)
-- which, all else equal, will be a slightly slower function. (Discrete
replication can be faster than pure exponential replication only if tdiscrete
< t ln(2).)
Replicating populations limited to activity only at the perimeter of the
expansion wave, or in regions of high replibot number density, may achieve
only polynomial growth rates [19], which are
even slower.

In order to estimate t = tconv,
the time required for total conversion of the biosphere to replibots plus
waste sludge, we must first estimate t.
Drexler [4] has calculated that a readily-envisioned
multistage molecular manufacturing system could manufacture its own mass
in t ~ 1000 seconds.
However, nanoreplicators need not be capable of general purpose manufacturing,
but may be optimized solely for replication of their own substance. A molecular
manipulator designed by Drexler [4] that is
suitable for molecular assembly pick-and-place operations consists of 4
million atoms excluding support base, power, control, and other necessary
structures, and is designed to perform ~106 atomic-precision
molecular pick-and-place operations per second, assuming arm-tip movement
at 1 cm/sec over minimal 10-nm arcs each cycle. Freitas [6]
estimates that a basic autonomous nanoassembler using two Drexler manipulator
arms and incorporating a simple onboard nanocomputer might require at least
~70 million atoms (~1 gigadalton), suggesting a minimum replication time
t
~ 100 seconds. (The smallest independently viable cells are thought to
have a molecular weight of order ~1 gigadalton, e.g., minimum diameter
~140 nm[72, 73].)

It is difficult to imagine how an ecophagic replicator capable of successfully
assimilating natural biomatter of all existing varieties could be much
simpler than this. However, it is possible that molecular manipulators
might be slewed at speeds up to ~100 cm/sec, perhaps giving t
~ 1 sec, but at the cost of steeply rising energy dissipation [4]
which greatly increases waste heat production and system operating temperatures,
and reduces nanoreplicator reliability due to larger thermally-excited
displacements, thermal damage rates, and phonon-mediated drag [4].
For example, a 10-nm force sensor measuring 10 pN at an operating temperature
of 300°K has a 0.2% probability of erroneous measurement; this probability
jumps to 3% at 500°K and 16% at 1000°K [4].
Hence, t ~ 1 sec
appears to be a rather aggressive and probably unachievable lower limit.

Carbon inventory in the global biomass has been estimated as 1.1 ×1015
kg (Table 1). Life is ~23% carbon by weight, so the
total global biomass can be estimated as Mbio
~ 5 ×1015 kg. Starting from a single 70-million-atom
replicator of mass ~1 gigadalton [6] or Minit
~ 1.7 ×10-18 kg, and taking
t
~ 1 sec and Mrepl
= 0.23
Mbio ~ 1.2 ×1015
kg, then tconv ~
76 sec. Adopting a more reasonable t
~ 100 sec, tconv ~ 7600
sec. For comparison, the fastest known replicators found in nature are
certain bacteria which have a mean generation time of t
~ 900-1200 sec (15-20 minutes) [27]. However,
these bacteria are capable of digesting only certain limited forms of biological
matter and have very severe operational restrictions including proper temperature,
pH, and so forth. They are not bio-omnivorous.

4.0 Dispersal Velocity Limitation

The expansion of any population of replicating systems is also fundamentally
restricted by the expansion velocity of the outermost envelope which defines
the maximum physical extent or dispersion of the growing population. No
population of ecophagic objects can disperse more quickly than its growth
medium -- in this case, the terrestrial biosphere -- will permit. Thus
for a two-dimensional growth medium on the surface of a sphere (e.g., the
Earth), the time required for complete biospheric conversion starting from
a single initial release site must be at least the minimum time required
for the replibots to travel exactly half of a great circle route across
the spherical surface, since the expanding wavefront of conversion is moving
around the globe in all compass directions simultaneously. This minimum
conversion time may be crudely approximated as:

tspread³
vrepl-1
(4pREarth2
/ N)½

(2)

assuming tspread >> t,
where the mean planetary radius REarth
= 6.37 ×106 meters,
N
is the number of initial replibot release sites, and vrepl
is the maximum nanoreplicator linear dispersal velocity. For isolated replibots
lacking significant aeromotive capabilities, dispersal velocity will be
limited approximately to the mean global wind speed, perhaps vrepl
~ 10 m/sec, ignoring the narrow 30-75 m/sec jet streams at 9-16 km altitude
[94]. This is also near the maximum feasible velocity
for nanorobotic flyers operating in the viscous regime, based on maximum
attainable endogenous power densities [6].

Assuming a single initial release site (N
= 1) and taking vrepl
~ 10 m/sec, then tspread
~ 2 ×106 sec. However, a more efficient biosphere conversion
strategy would incorporate the simultaneous release of numerous "seed"
replibots distributed uniformly throughout the terrestrial biomass, thus
reducing the required maximum extension of each expanding replication domain
from neighboring replibot release sites. Large numbers of replibots could
be transported by high-velocity airborne macroscale carrier vehicles to
distant sites around the world and then released, crudely analogous to
a jet aircraft scattering printed leaflets over a civilian area during
wartime. Nanoreplicator progeny tasked with the conversion of biomass to
nanomass within such smaller substrate domains have much less distance
to travel to complete their purpose. Minimum biomass conversion time scales
roughly as N½, where
N
is the number of independent initial replicator domains, as reflected in
Table
2 generated from Eqn. 2:

Table 2.Minimum Replibot Dispersal Time as a Function of theNumber of Uniformly-Distributed Replibot Release Sites

# of Release Sites
(N)

Mean Distance Between
Neighboring Release Site

Min. Global Dispersal Time,
tspread(for vrepl
= 10 m/sec)

1

2 × 107 meters

30 days

102

2 × 106 meters

3 days

104

2 × 105 meters

6 hours

106

2 × 104 meters

40 minutes

108

2 × 103 meters

200 sec

1010

2 × 102 meters

20 sec

1012

2 × 101 meters

2 sec

This analysis suggests that the limitations on biosphere conversion
rate imposed by dispersal velocity are readily overcome by employing a
sufficient number of release sites, and do not, by themselves, prohibit
ecophagic conversion times on the order of ~1000 seconds or less. In principle,
very sophisticated biovores could facultatively aggregate into macroscale
assemblages to escape the viscous flight regime, theoretically permitting
aerodynamic or even suborbital flight velocities up to 100-1000 m/sec.
Replicators incapable of aerial transport will experience significantly
longer dispersal times.

In practical surface deployments, major distribution nonuniformities
will exist because some areas have significantly larger carbon inventories
than others [28]. For example, a map of the global
annual net primary production (NPP) of photosynthetically fixed carbon
on land shows NPP ranging from 0.1-1.5 kg/m2-yr of carbon, with
25% of the land surface area without permanent ice supporting an NPP
> 0.5 kg/m2-yr and an average of 0.426 kg/m2-yr
on land [21]. The oceans, which cover ~70% of
Earth's surface and show carbon fixation activity averaging only 0.14 kg/m2-yr
[21], contain a mere 0.02% of the entire planetary
biomass, compared to 99.98% on land.

The uneven geographical distribution of carbon inventories [28]
and solar power availability [83] along with
possible element shortages (Tables 3 and 5)
may produce significant geographical variation in replication rates.
A detailed analysis of such variation is beyond the scope of this paper
but likely would place upper limits on replication speed in many environments.

5.0 Energy
and Materials Requirements Limitations

The need for energy is another fundamental limit on the speed at which
biospheric conversion can take place. During ecophagy, the richest source
of energy is likely to be chemical energy derived from the assimilation
of biomolecules found in the biosphere. For example, a biomass density
of ~10 kg/m2 on land [20, 21]
typically having ~107 J/kg of recoverable chemical energy [6]
implies an available energy density of ~108 J/m2
at the terrestrial surface. By comparison, visible-spectrum sunlight at
noon on a cloudless day (Isolar
~ 100-400 W/m2 [6]) may provide
at most ~107 J/m2 over the course of an 8-hour work
day. Other sources of scavengable energy such as radionuclides are much
scarcer (Section 2.0). Note that
the complete combustion in air of a mass of glucose equal to
Mbio
would consume ~5.3 ×1015 kg O2, only 0.5% of
the ~1.1 ×1018 kg of oxygen contained within Earth's ~21%
O2 atmosphere. Hence oxygen-dependent ecophagy will not be oxygen-limited.

Interestingly, diamond has the highest known oxidative chemical storage
density because it has the highest atom number (and bond) density per unit
volume. Organic materials store less energy per unit volume, from ~3 times
less than diamond for cholesterol, to ~5 times less for vegetable protein,
to ~10-12 times less for amino acids and wood [6].
Since replibots must build energy-rich product structures (e.g. diamondoid)
by consuming relatively energy-poor feedstock structures (e.g., biomass),
it may not be possible for biosphere conversion to proceed entirely to
completion (e.g., all carbon atoms incorporated into nanorobots) using
chemical energy alone, even taking into account the possible energy value
of the decarbonified sludge byproduct, though such unused carbon may enter
the atmosphere as CO2 and will still be lost to the biosphere.

The speed of biospheric conversion can also be limited by the abundances
of chemical elements available in the environment for conversion into nanomass,
as compared to the relative quantities of each element that are required
by the nanorobot for replication. (In replicator engineering, this is the
"materials closure" issue [19]; in chemistry,
it is called "stoichiometry.") In the gray goo scenario, nanorobot replication
occurs on the Earth's surface, so any elements which are in short supply
in the biosphere might alternatively be obtained from nearby topsoil or
crustal rocks, although this may impose an additional logistical overhead
on replicative processes. Hence only the concentration of the most abundant
of these two sources may act as a significant limit to replication speed.
Traditional diamondoid nanomachinery designs [4]
have employed 8 primary chemical elements, as summarized in Table
3 (more details in Table 5); Table
3 also gives the associated biological [6]
and crustal [5] abundances for each element.

Dividing the lowest and highest nanorobot requirement by the highest
available environmental abundance gives tmult,
the required increase in replication time due to scarcity of a chemical
element required for replication. Inspection of Table
3 reveals that sulfur appears to be in the shortest supply relative
to nanorobot requirements (at least for current primitive designs), possibly
increasing replication time t
by a factor of up to 41 while the device waits for sufficient sulfur atoms
to be accumulated from the environment. Other elements possibly in somewhat
limited supply include P, N and F, although the impact of any of these
elements on replication time can probably be minimized by judicious nanorobot
composition design choices.

As a general rule, ecophagic nanorobot replication time is longer in
direct proportion to the extent that nanorobot elemental requirements exceed
the availability of the scarcest element in the consumable substrate, in
comparison to the theoretical nanorobot replication time on a perfectly
compositionally-matched substrate [19]. This
phenomenon is commonplace in biology. For instance, it is well-known that
phytoplanktonic growth in the open oceans is iron-limited [29].

The highest near-term risk could come from relatively simple single-behavior
replibots whose niche is a high-energy substrate of uniform composition
which affords a rapid vector for the dispersal of the replicators [79].
The classic example is tire rubber and asphalt tar binder; cars,
trucks and airplanes roll on roads and tarmacs worldwide. If the ~4 million
miles of paved roads in the U.S. [80] represent
~25% of the global total, then road asphalt mass worldwide is ~3
×1013
kg, or ~0.6% Mbio;
the global rubber tire population of ~10 billion tires stockpiled, in use
or discarded in scrap heaps [80, 82]
adds another ~0.003% Mbio.
Other vectors with similar properties include cotton, polyester or other
uniform textiles [79], insulation on electrical
wiring, and paper money. Regular monitoring and decontamination procedures
may thwart these threats.

6.0 Ecophagic Thermal
Pollution Limits (ETPL)

A more restrictive limitation on the maximum speed of biomass conversion
to nanomass is the generation and release of process waste heat into the
environment during ecophagy. If there are too many nanoreplicators working
all at once, the waste heat they generate can begin to warm up the environment.
In some cases, the environment could become so hot that the biospheric
conversion process can no longer proceed.

In the crude analysis that follows, we assume that after some number
of prior replication cycles, the replibots have converted roughly half
of the biosphere to nanoreplicator mass. In the next and final replication
cycle, the energy extractable from the remaining half of the global biomass
will be consumed as each existing nanorobot replicates itself once more
for the last time, thus promptly doubling the existing population and completing
the global conversion of biomass into nanomass.

In this case, the total heat energy released at Earth's surface is Ptotal
= Pnano + Psolar,
where Pnano is the waste
heat generated by the replibots as they emit Ehalf
joules in the last replicative cycle of duration tlast,
with Pnano = Ehalf
/ tlast,
and where the total solar insolation on Earth's cloudless surface that
is subsequently thermalized is Psolar
~ 1.75 ×1017 W. Neglecting the heat-trapping effects of
greenhouse gases and the minor contributions from the geological heat flow
at Earth's surface, the temperature at the terrestrial surface is given
approximately by the Stefan-Boltzmann relation:

Ptotal = 4pREarth2ersTEarth4

(3)

where er is terrestrial
surface emissivity, taken here as 0.97 (e.g. carbon black) to maximize
heat emission at the lowest possible temperature,
s
is the Stefan-Boltzmann constant (5.67 ×10-8
W/m2-K4), and TEarth
is the mean surface temperature of Earth. The minimum last-replication
time that will allow a global temperature of TEarth
or lower to be maintained throughout the final conversion cycle is given
by:

tlast
= Ehalf / [4 pREarth2ersTEarth4-Psolar]

(4)

~ Ehalf / [ (2.8 ×107)
TEarth4-
(1.75 ×1017) ]

What is an appropriate maximum operating temperature limit for nanoreplicators
that must forage for organic substrate in order to replicate? The softening
point for sapphire, an oft-mentioned substitute building material for diamond
because of its high strength, high-temperature tolerance, and inability
to burn in oxygen, is 2070°K [30], probably
near the upper limit in any reasonable ecophagic nanorobot design scenario
especially given the seriously negative impact of higher temperatures on
nanorobot reliability and functionality (Section
3.0). The combustion temperature of diamond in air is usually given
as 870-1070°K [31].

However, such elevated surface temperatures, while perhaps acceptable
for diamondoid nanomachines in some circumstances, will immediately volatize
and incinerate most of the natural organic feedstock upon which the nanoreplicators
must feed. The minimum ignition point of wood, paper, or diesel fuel in
air has been given as low as ~500°K [68],
and glucose caramelizes [6] at 433°K --
caramelization is not oxidation but rather is a decomposition reaction
that includes polymerizations and covalent bondmaking that could render
this substrate material somewhat less accessible to the replibots. A still
lower temperature threshold is the boiling point of water at 373°K;
above this temperature, living things will boil, thus denying ecophagic
nanoreplicators access to solution-based chemical processes at normal atmospheric
pressures, which could be an important restriction.

The waste heat energy released globally in the last replicative cycle
may be estimated as Ehalf (qDbio)
Mbio,
where Dbio is the energy
density of the organic feedstock material and q
is the energy conversion ratio for its transformation into nanomass. For
example, Dbio = 16 MJ/kg
for glucose, 17 MJ/kg for vegetable protein, 18 MJ/kg for animal protein,
19 MJ/kg for wood, and 39 MJ/kg for fats [6].
However, these figures refer to the energy content of the organic feedstock,
not to the energy that must be consumed (and the waste heat subsequently
thermalized) in order to build a kilogram of nanomass. Drexler [4]
estimates that the typical energy dissipation caused by chemical transformations
involving carbon-rich materials will be Ediss
= (qDbio)
~ 100 MJ/kg of final product using readily-envisioned irreversible methods
in systems where low energy dissipation is not a primary design objective.
This figure corresponds roughly to the strongest covalent bond energies
(e.g., 1190 zJ/bond for C=C, 1327 zJ/bond for C=O, and 1594 zJ/bond for
CºC [4]),
and is roughly of the same order as the thermodynamic heat of formation
of diamond from CO2(g), ~33 MJ/kg [5].

Drexler [4] claims that energy dissipation
may in theory be as low as Ediss
~ 0.1 MJ/kg "if one assumes the development of a set of mechanochemical
processes capable of transforming feedstock molecules into complex product
structures using only reliable, nearly reversible steps." 0.1 MJ/kg of
diamond corresponds roughly to the minimum thermal noise at room temperature
(e.g., kT
~ 4 zJ/atom at 298°K). R. Merkle [32]
also conjectures that near-zero energy dissipation is in principle possible
in certain special circumstances, a possibility that should be investigated
in the present context in a future theoretical study. However, near-term
nanochemistries are unlikely to be significantly more efficient than natural
enzyme chemistries, which have been evolving for efficiency over eons;
the terrestrial biosphere fixes ~1.2 ×1014 kg/yr of biomass
carbon [21] with a ~1.4 ×1014
watt energy input [6], or Ediss
~ 38 MJ/kg of carbon.

Using Eqn. 4, the minimum last-replication time
can be calculated for various plausible values of Ediss,
wherein the mean terrestrial temperature will not exceed the chosen value
of TEarth during ecophagy,
as given in Table 4:

Table 4.Minimum Last-Cycle Replication Time for Ecophagic Nanorobots as
a Function of Replication Energy Efficiency and the Resulting Global
Temperature

Setting aside Merkle's conjecture, Table 4
suggests that if phenomenally efficient reversible molecular manufacturing
techniques become available -- e.g., Ediss
~ 0.1 MJ/kg -- the final replicative cycle of global ecophagy could proceed
as quickly as ~1000 seconds while just avoiding incinerating the organic
feedstock or boiling environmental water. However, there currently exist
no known designs which would be capable of achieving such highly energy-efficient
nanoassembly operations.

More probably, highly dissipative molecular manufacturing designs are
likely to be implemented during the early and intermediate years of molecular
nanotechnology development. Such designs are also likely to be necessary
for the very complex machines needed to implement biovorous replication
given the enormous variety of chemically diverse natural biological substrates.
Assuming current and foreseeable energy-dissipative designs requiring ~100
MJ/kg for chemical transformations (most likely for biovorous systems),
complete ecophagy that proceeds slowly enough to add ~4°C to global
warming (near the current threshold for immediate climatological detection)
will require ~20 months to run to completion. Faster ecophagic devices
will run hotter, allowing quicker detection by policing authorities.

The conversion of biomass to nanomass may proceed according to Eqn.
1 up to the ecophagic thermal pollution limit (ETPL) whereupon the
specified maximum global temperature TEarth
is attained, after which the replication time must approximately double
after each population doubling, ultimately reaching tlast
in the final doubling, as described by Eqn. 4. Total
time spent in the ETPL-limited regime is ~ 2 tlast.
For example, taking t
= 100 sec, TEarth = 300°K,
and
Ediss ~ 100 MJ/kg, the
transition to the ETPL regime occurs when total global nanomass reaches
~5 ×1010 kg, or only 0.001% of total global biomass, and
the last ~17 population doublings remain to be completed over a time span
of ~2
tlast
= 2 ×107 sec (~7 months). This is also the optimum strategy
for an ecophagic population that is attempting to evade premature detection
by maintaining a low thermal emissions profile. Constant ecological surveillance
for any evidence of ecophagic activity is an appropriate policing measure
to provide adequate early warning to the existence of this threat.

Note further that the presence of natural and anthropogenic greenhouse
gases in the Earth's atmosphere will amplify any heating effects, helping
to make ecophagic activities more immediately visible in its earlier stages.
(In theory, a large enough replibot population could actively manage terrestrial
albedo or global greenhouse gas concentrations, but these activities would
themselves generate still more waste heat.) Additionally, using the actual
current mean value of er
= 0.69 for terrestrial emissivity in Eqns. 3 and 4,
rather than the much higher value of er
= 0.97 for carbon black assumed in calculating Table
4, the last-cycle time tlast
increases by another ~40%, giving still more time for defensive instrumentalities
to be brought to bear on the situation.

Assuming the surface biomass is compositionally similar to wood (Dbio
~ 19 MJ/kg), prompt consumption (e.g., combustion) of the entire biosphere
would release Qwaste = MbioDbio
~ 1023 J of energy. The combined heat capacity of planetary
oceans (1.36 ×1021 kg [6]
at 4200 J/kg-K [6] = 6 ×1024
J/K) and land (~4 ×1020 kg/km crustal landmass
at, e.g., 833 J/kg-K for silica [90] = 3 ×1023
J/km-K) is ~1025 J/K, so in principle
Qwaste,
ideally distributed, could be absorbed with a negligible rise in global
temperature, ~0.01ºK -- although even a slight rise in ocean temperature
could increase mean worldwide humidity, greatly amplifying global warming
because water vapor is the most effective greenhouse gas [91].
However, in the instant scenario, the replibots are assumed to be in intimate
contact with the biomass which they are consuming -- not with the vast
volumes of sea or land. Air is an excellent insulator (see below),
and the thermal conductivity of wood is ~4 times higher than for air, so
replication waste heat energy will be conducted primarily into the nanorobot
population and the proximate biomass that is being consumed. The
heat capacity of diamond and organic materials (e.g. wood, rubber, etc.)
is ~2 MJ/m3-K [6], or ~800 J/kg-K
for the biomass/nanomass aggregate as dry mass or up to 3200 J/kg-K assuming
70% water content. Taking the higher figure, the total heat capacity
of the biomass/nanomass aggregate is Cbn
~ 3200 J/kg-K × Mbio
= 2 ×1019 J/K. Adding Qwaste
to this aggregate would raise its temperature by DT
~ Qwaste / Cbn
~ 5,000ºK.

Similarly, air conduction is unlikely to significantly reduce the ETPL
limits. Waste energy can be absorbed by atmospheric heat capacity
(5.27
×1018 kg [6] at 988
J/kg-K [6] = 5 ×1021 J/K)
only if said heat energy is delivered to the atmosphere and thoroughly
mixed via conduction, convection, or radiative transfer. But the
thermal conductivity (Kt)
of air is very poor. Consider a layer of air H
meters thick and area A, with temperature
differential DT
on opposite faces, with power flow through the layer of P
= KtADT
/ H = Qwaste
/ tburn, where power
is generated by consuming the ecosphere in a time tburn,
so the temperature differential across the layer is DT
= QwasteH
/ (KtAtburn).
With a thin layer of replibots coating the foliage on Earth's surface,
generating heat only on the "skin" of the biosphere, there will be a nonconvective
stagnant layer of air trapped for long periods near the surface that is
poorly mixed by winds. In weather modeling this viscous sublayer,
called the roughness parameter, may be ~0.01-300 cm thick [84-86]
(e.g., 0.01 cm over water surface, 0.1 cm over short grain, 10 cm over
prairie grass, 100 cm over grain crops [85]),
and sometimes is taken as ~10% of the height of the obstacle [87].
Assuming H ~ 1 cm layer and taking
Qwaste
= 1023 J,Kt
= 2.5 ×10-2 W/m-K for air [6],
A
= 5.10 ×1014 m2 for Earth, then DT
~ 7 ×107 / tburn.
Thus, consuming Mbio in
tburn
= 104 sec nominally produces a temperature differential across
the 1 cm layer of
DT
~ 7000ºK (and violates our nonconvection assumption);
assuming tburn = 6 months,
then DT
~ 4ºK, detectable using current orbital surveillance assets given
a normal tropospheric thermal gradient of 0.006-0.009ºK/m [88].
(Vertical temperature gradients below 0.010ºK/m are considered subadiabatic,
producing downward buoyancy forces [89].)
These crude estimates provide an approximate indication of the magnitudes
involved, but the details of convective vertical mixing and its possible
meteorological consequences during ecophagy are beyond the scope of this
paper and should be investigated further.

7.0 Homeostatic Resistance
to Ecophagy

Over long time periods, natural ecosystems are believed to have a nearly
balanced carbon budget, with photosynthetic uptake equal to respiratory
release [33]. From the ecological perspective,
the insertion of carbon-absorbing artificial devices into the environment
represents a new sink in the homeostatic global carbon cycle, in addition
to the natural carbon sinks such as forests [34,
35].
Most of terrestrial biomass consists of plants, especially trees, though
nearly half of all biomass may consist of bacteria, mostly in soils (up
to ~1015 cells/m3) and subsurface sediments and rocks
down to ~3 km depth [12,
38];
there are ~5 ×1030 bacteria on Earth [39].
Conversion of living plant biomass to diamondoid nanomass by nanoreplicators
thus may reduce the ability of the surviving plant population to remove
carbon dioxide from the atmosphere. Unless carbon dioxide levels in the
atmosphere are directly regulated by the active robotic nanomass, CO2
levels will begin to rise, which in turn may increase the growth rate of
plants. In a few experimental studies [40],
elevated CO2 has been shown to stimulate plant growth at least
temporarily, even under serious nutrient shortage, although one experiment
[41] challenges this supposition. If slow-moving
nanoreplicators consume biomass only very slowly, the consumed biomass
may be regenerated as new plant growth is stimulated worldwide.

What is the minimum ecophagic biomass removal rate necessary to overcome
the resulting carbon-sequestration response of the natural ecology? One
study [20] found that deforestation in the low
latitudes during 1990 resulted in forest area expansion and growth in mid-
and high-latitude forest that sequestered ~7 ×1011 kg
of carbon (e.g., creating ~3 ×1012 kg of extra biomass)
in one year. Estimates of unrealized global forest carbon conservation
and sequestration potential suggest a biologic capability of 1-3
×1012 kg/yr (e.g., 4-13 ×1012
kg/yr of biomass) for more than a century [20].
Global oceans are believed to absorb ~2 ×1012 kg/yr of
anthropogenically-produced carbon, creating ~9 ×1012 kg
of new biomass per year [20]. This gives a worldwide
carbon sink of ~5 ×1012 kg/yr of carbon [42]
and thus a global biomass recovery of at least ~2 ×1013
kg/yr. The upper limit is probably closer to the global net primary biomass
production of ~5 ×1014 kg/yr [21].
(Indeed, natural variations of ~1014 kg of atmospheric carbon
(equivalent to ~6 ×1014 kg of biomass) were recorded over
a ~600-year period during the last three glaciation cycles [43].)
Thus it appears that a long-term ecophagic biomass removal rate exceeding
0.2-5
×1014 kg/yr (~0.4%-10%/yr of the global biomass)
may be necessary to overpower the natural ecological restorative forces.

8.0 Additional Scenarios

Four related scenarios which may lead indirectly to global ecophagy have
been identified and are described below. In all cases, early detection
appears feasible with advance preparation, and adequate defenses are readily
conceived using molecular nanotechnologies of comparable sophistication.

8.1 Gray Plankton

The existence of 1-2 ×1016 kg [24]
of global undersea carbon storage on continental margins as CH4
clathrates and a like amount (3.8 ×1016 kg) of seawater-dissolved
carbon as CO2 represent a carbon inventory more than an order
of magnitude larger than in the global biomass (Section
3.0). Methane and CO2 can in principle be combined to form
free carbon and water, plus 0.5 MJ/kg C of free energy. (Some researchers
are studying the possibility of reducing greenhouse gas accumulations by
storing liquid [44] or solid [45]
CO2 on the ocean floor, which could potentially enable seabed
replibots to more easily metabolize methane sources.) Oxygen could also
be imported from the surface in pressurized microtanks via buoyancy transport,
with the conversion of carbon clathrates to nanomass taking place on the
seabed below. The subsequent colonization of the land-based carbon-rich
ecology by a large and hungry seabed-grown replicator population is the
"gray plankton" scenario. (Phytoplankton, 1-200 microns in size, are the
particles most responsible for the variable optical properties of oceanic
water because of the strong absorption of these cells in the blue and red
portions of the optical spectrum [37].)

The gray plankton replicator waste heat signature is readily detected
at an early stage. The temperature of most of the ocean is near ~4°C
-- for example, ~1.6°C at 3627 m on the floor of Monterey Bay [44].
Typical ocean column thermal gradients are ~0.02°K/m in the top 300
m (1-30 atm) and ~0.006°K/m from 300-1000 m depth (30-100 atm) [44].
A near-seafloor water temperature change of DT
= 1°K over a depth range of L =
100 m would be clearly distinguishable from natural variations even using
contemporary instrumentation [44], and would
evidence an increased seabed power release of Irepl
~ Kt (DT
/ L) ~ 0.005 W/m2, taking
thermal conductivity as Kt
~ 0.5 W/m-K for seawater at 4°C. Thus the threshold for seafloor replibot
detectability, assuming global seabed area is Aseabed
~ (70%) 4pREarth2
= 3.6 ×1014 m2, is Pmin
= IreplAseabed
~ 2 ×1012 watts worldwide or a global replibot population
of mass Mmin ~ Pmint
/ Ediss ~ 20 ×106
kg assuming Ediss ~ 100
MJ/kg and
t = 1000
sec. (Faster replicators are detectable at lower population masses.) Thus
bottom-dwelling gray plankton can be detected before they have consumed
more than 10-9 of the total oceanic
abiotic carbon supply.

Direct census sampling of the seafloor may also allow early detection,
although nanorobotic samplers will have to contend with a significant number
of false targets in the oceanic environment. These false targets may include
0.1 micron small colloids (~7 ×1014 m-3)
and viruses (~3 ×1013 m-3),
0.2-0.3 micron heterotrophic bacteria (~1012 m-3),
0.3 micron large colloids (~1013 m-3),
1 micron cyanobacteria (~1010 m-3),
2-3 micron small phytoplankton (~108 m-3),
larger phytoplankton (e.g., 10 micron cells ~106 m-3),
and zooplankton (e.g., 50 micron cells ~103 m-3)
[36-38]. At
the minimum detectable global mass of Mmin
= 20 ×106 kg estimated above, the number density of gray
plankton on the seabed floor is Ngp
~ Mmin / (Aseabedmgp)
~ 2 ×107 m-2, assuming
~1 micron gray plankton replicators each of mass mgp
~ 3 ×10-15 kg. In this scenario,
the bottommost 1 mm of the ocean column above the seabed would contain
roughly equal numbers of > ~1-micron natural cells and ~1-micron artificial
bottom-dwelling gray plankton devices. If not largely confined to the sea
floor during most of their replication cycle, the natural cell/device ratio
could increase by many orders of magnitude, requiring a more diligent census
effort. Census-taking nanorobots can alternatively be used to identify,
disable, knapsack or destroy the gray plankton devices.

8.2 Gray Dust (Aerovores)

Traditional diamondoid nanomachinery designs [4]
have employed 8 primary chemical elements, as detailed in Table
5 along with the associated atmospheric abundances [46]
of each element. (Silicon is present in air as particulate dust which may
be taken as ~28% Si for crustal rock [5], with
a global average dust concentration of ~0.0025 mg/m3). The requirement
for elements that are relatively rare in the atmosphere greatly constrains
the potential nanomass and growth rate of airborne replicators. However,
note that at least one of the classical designs exceeds 91% CHON by weight.
Although it would be very difficult, it is at least theoretically possible
that replicators could be constructed almost solely of CHON, in which case
such devices could replicate relatively rapidly using only atmospheric
resources, powered by sunlight. A worldwide blanket of airborne replicating
dust or "aerovores" that blots out all sunlight has been called the "gray
dust" scenario [47]. (There have already been
numerous experimental aerial releases of recombinant bacteria [48].)

Two independent constraints on gray dust replication speed are materials
and energy availability, and both methods suggest that t
~ 10,000 sec for 1-micron replicators and ~1000 sec for 0.1-micron replicators.
The analyses are as follows.

First, the mass current Mcurr
through the surface of a spherical nanorobot of radius Rnanois
equal to the number of gas molecules/sec that collide with the fraction
f
~ 10% of the nanorobot surface that consists of binding sites for those
molecules, times the mass per gas molecule
mgas,
divided by the number of collisions required for binding to occur, or Nencounter
~ 100 [6]; that is:

Taking Rnano = 1 micron
and allocating each aelement
for the hypothetical CHON replicator as indicated in the second column
of Table 6 gives the values of t
shown at far right in Table 6. The limiting elements
are H and C, but C has the strongest impact on replication time, requiring
a t ~ 12,300 sec.
Since t scales
as Rnano, reducing Rnano
to 100 nm reduces
t
to ~1230 sec for this device. (Mechanical precompression and sortation
[6] of gas molecules might reduce t
by up to an order of magnitude but may impose partially offsetting internal
volume utilization inefficiencies.).

Second, the solar energy flux into the nanorobot, assuming that a fraction
f
of its surface is photosensitive with energy conversion efficiency e,
is Pnano = eIsolarf
pRnano2.
The energy required to build a nanorobot is Enano
~ MnanoEdiss,
hence the replication time is t
= Enano / Pnano,
or:

Since replication of an airborne CHON replibot is primarily carbon-limited,
in theory the entire global atmospheric carbon mass of ~5.2 ×1014
kg C is available for conversion into Mgd
= 8.4 ×1014 kg of CHON nanomass, assuming a 62% carbon
content by weight (Table 6). However, because the
machines are solar powered, the active population of gray dust nanorobots
is restricted to one optical depth of such devices. To a very crude first
approximation (e.g., ignoring contributions from scattered and reflected
photons), one optical depth occurs when the cumulative cross-sectional
area of the nanorobot population equals the surface area of Earth, so the
maximum total mass of continuously active CHON airborne nanorobots is:

Mtotal ~ (16p
/ 3) rRnanoREarth2
(kg)

(8)

= 1.4 ×1012 kg for Rnano
= 1 micron

= 3.7 ×1011 kg for Rnano
= 275 nm

= 1.4 ×1011 kg for Rnano
= 100 nm

Once the expanding nanorobot population reaches one optical depth (requiring
~0.2% of all atmospheric carbon, or ~3 months of current anthropogenic
airborne carbon releases), the replication rate of the gray dust ceases
to grow exponentially and becomes essentially constant -- a phenomenon
which may be called the "opacity brake effect." (One optical depth of uniformly
distributed Rnano = 275
nm aerovores represents a particle number density of ~5 ×108
m-3.) After the opacity brake point has been reached, a constant
nanomass production rate of Mtotal/t
~ 1.4 ×108 kg/sec ensues until exhaustion of the limiting
atmospheric carbon resource. Current instrumentation can detect ~1% variations
in the solar constant, so the limit for early bolometric detection is probably
~1% Mtotal, when ~0.002%
of atmospheric carbon has been converted to nanomass.

Dust monitors in late 20th-century wafer-fab clean rooms regularly measure
dust densities of ~10 particles/m3 at 0.5 microns and larger
[49], potentially allowing detection as early
as <10-8Mtotal
if more highly discriminating monitors can be developed. If the replibots
settle out on the planetary surface and continue replicating there (Section
8.3), they could deprive the ecology of needed sunlight without darkening
the sky, but their effects (e.g., a fine gray dust covering everything
on the surface) would also be detectable far sooner than the 1% Mtotal
point.

Since replication rate and opacity per unit nanomass vary inversely
with Rnano, the most efficient
gray dust replibot tasked with opacifying the atmosphere as quickly as
possible will have the minimum possible size. (Replication time varies
with thickness for a sheetlike nanorobot configuration.) The minimum replibot
size is driven by UV radiation damage rates on nanomachinery [4].
Consider the smallest possible replicator with mass Minit
= 1.7 ×10-18 kg (Section
3.0); constructed as a spherical shape of density r
= 2000 kg/m3, the radius of this core replicator is Rcore
~ 59 nm. The core is surrounded by a radiation shield of thickness d
and density ~r.
The most dangerous is UV-B at l
~ 280 nm which will conservatively be taken as ~5 W/m2 intensity
near ground level [4], equivalent to D0
= 7 ×1018 photons/m2-sec. The number of bonds
cleaved inside the nanorobot is Ncleave
= pRnano2qytlifeD0exp(-4pkxd
/ l), where
qy
is quantum yield (bonds cleaved / photons absorbed),
tlife
is mean time to failure, and kx
is extinction coefficient. kx
~ 2.26 for graphite at 280 nm [50], a 2250
kg/m3 semimetal that is probably the most UV-absorptive CHON
shield material.
qy = 10-4
to 10-1 for CHON polymers [51]
and various proteins, viruses and phages [52];
following Drexler [4], we adopt qy
~ 0.01 here (the exact choice is not critical to our conclusions). From
Eqn.
7, t ~ ctRnano,
where ct
~ 1010 sec/m. Taking tlife
= tnt,
where nt
is the number of offspring constructed before replibot failure, and assuming
that Ncleave³
1 implies device failure [4], then:

From Eqns. 1 and 8, and neglecting
dispersal velocity limitations (Section
4.0) the minimum possible time to reach some fraction fopac
of global atmospheric opacity is:

topac = t
ln(4 fopacREarth2
/ Rnano2) (sec)

(10)

For airborne CHON replibots with Rnano
= 275 nm and t
~ 2750 sec, 1% of opacity is reached in topac
~ 1.85 days, 100% opacity in 2.0 days, leaving a response time of ~3.5
hours between first detection at 1% opacity and complete opacity at 100%.
If uniformly distributed throughout the atmosphere, the dust density at
100% opacity would amount to ~0.085 mg/m3 for 275-nm nanorobots,
about equal to the typical ~0.05 mg/m3 dust density normally
found in the air of most industrialized Western cities [69].

After 100% opacity is reached, another tend
= t (Mgd-Mtotal)
/ Mtotal = 72 days would
be required to convert the remaining atmospheric carbon resource into nanomass.
However, post-opacity the gray dust replication rate is no longer exponentiating
so the defensive nanorobots can quickly catch up.

The most efficient cleanup strategy appears to be the use of air-dropped
non-self-replicating nanorobots equipped with prehensile microdragnets.
Consider a planetwide dragnet comprised of a square mesh of fibers, with
mesh aperture size lmesh,
mesh fibers of thickness dfiber,
and total dragnet area Anet
covering Earth's entire surface area AEarth
= 4pREarth2
= Anet. Minimum fiber thickness
is dfiber (pairlmesh2
/ 4 sfiber)½,
where
pair 2 atm is
the maximum air pressure resisting movement of the net through the air
and fiber failure strength is very conservatively taken as sfiber
~ 1010 N/m2 for carbon nanotubes. For lmesh460 nm (smallest possible gray dust replibot, see above), dfiber 1 nm. Simple geometry gives the total volume of required square-grid
dragnet as:

Vdragnet ~ 2 dfiber2
[(Anet½)
+ (Anet / lmesh)]
(m3)

(11)

Taking Anet = AEarth
= 5.10 ×1014 m2, lmesh
= 460 nm and dfiber = 1
nm, then
Vdragnet = 2200
m3. This dragnet may be carried aloft by a fleet of Nbot
= Vdragnet / fvVbot
spherical defensive nanorobots, each of which uses some fraction fv
of its internal storage volume to hold a piece of the dragnet, where individual
defensive nanorobot volume is Vbot
= (4/3)pRnano3.
Taking fv = 5% and Rnano
= 0.62 micron, Vbot = 1
micron3 and Nbot
= 4.4 ×1022 defensive nanorobots of total mass
~VbotrNbot
= 8.8 ×107 kg (of which ~4.4 ×106
kg is dragnet). Thus a single 88-kg payload of non-self-replicating defensive
nanorobots launched from each of 106 deployment sites worldwide
(mean site separation ~23 km, ~one per town) to an altitude just above
the gray dust replibots can deploy an Earth-covering net, which then descends
through the air, selectively filtering out the gray dust replibots. The
time required for this dragnet to sweep the entire atmospheric volume of
Earth once is
tsweep ~ Vair
/ (4pREarth2vnano)
~ 24 hours, taking nanorobot aeromotive velocity vnano
~ 0.1 m/sec for power densities appropriate to solar powered nanodevices
[6] and Vair
~ 4.36 ×1018 m3 at ~1 atm pressure and room
temperature. Possible false targets that may be encountered during the
sweep include airborne fungal spores at 10-500 m-3
indoors and 100-1000 m-3 outdoors
[53]; bacteria at 0-500 m-3
indoors, 179-1083 m-3 outdoors [53],
and ~140 m-3 up to ~3 km altitude
[38]; and inert dust particles of various
sizes peaking in number density near ~20 nm [46],
in concentrations ranging from 10 m-3
in semiconductor fab plant clean rooms up to 2 ×107 m-3
in quiet country air, 6 ×107 m-3
over residential city air, 1.5 ×108 m-3
in the worst congested downtown city air, and >2.7 ×108
m-3 in rooms with smokers present
[49, 54]. Of course,
multiple cleansing sweeps may be required, insecta
and birdb management and biocompatibility
protocols must be devised, exterior surfaces must be appropriately hydrophobic
to avoid providing condensation nuclei for cloud and fog formation, and
so forth.

The total machine volume of one optical depth of 275-nm gray dust replibots
is 1.9 ×108 m3, making an average cleanup requirement
of only ~4500 micron3 of targets per defensive nanorobot. A
spherical knapsack comprised of additional mesh material having an enclosed
volume of 4500 micron3 adds only 11% to the onboard mesh storage
requirement. Each defensive nanorobot deploys a (110 micron)2
~ 12,100 micron2 section of the planetwide dragnet. In theory,
if this section were curved into a huge spherical knapsack, it would make
a storage volume of 125,000 micron3 -- enough to hold the equivalent
of ~28 optical depths of gray dust replibots during passage through locally
dense clouds of target airborne nanoreplicators.

Each defensive nanorobot requires ~66 nN of motive force and ~6600 pW
of onboard power to overcome drag loss [6]
on the ~5.3 cm length of dragnet fiber that it is passing through the air
at 0.1 m/sec. This power is provided by a rear-deployed, 30% efficient,
55 micron2, ~10 nm thick solar collector film that stows in
a 0.55 micron3 volume before deployment and adds only ~45 pW
to drag power after deployment. When fully deployed, the defensive fleet
contributes <0.5% additional atmospheric opacity, and clears air for
an energy cost of ~5.8 J/m3 of contaminated atmosphere, per
pass. Defensive nanorobot locomotion in the viscous flight regime may be
provided by screw drives, viscous anchoring via the prehensile dragnet,
or other means [6].

The Stokes settling velocity [6] in air
is ~240 micron/sec for Rnano
= 1 micron, ~20 micron/sec for
Rnano
= 275 nm and ~5 micron/sec for Rnano
= 100 nm, giving 10-km passive fall times (in still atmosphere) of 1.3
years, 16 years and 67 years, respectively.

Alternative airborne or ground-based atmospheric filtration configurations
that could permit more rapid filtering are readily envisioned. For example,
since drag power varies as the square of the velocity, then by increasing
mesh volume 10,000-fold while decreasing airflow velocity 100-fold, total
drag power remains unchanged but whole-atmosphere turnover proceeds 100-fold
faster, e.g., ~15 minutes.

a There are
~1018-1019 insects on Earth [75-77].
The average insect devotes ~35% of body volume to its respiratory system
[78], which is mostly gas-phase diffusional
but with some very primitive active ventilation. If average insect
volume is ~0.6 mm3 [77], then the worldwide
insect population has ~2 × 109 m3
of tracheal air volume which could accumulate ~1016 aerovores
if insects are exposed to replibot-contaminated air at a concentration
equivalent to ~1% atmospheric opacity. In this case ~10-9
of the global aerovore population resides inside insects (~1 replibot per
1000 insects at 1% opacity), requiring careful quarantine or inspection
and release protocols for insects passing through the dragnet.

b There are ~300
billion birds on Earth [70]. The average
bird devotes 20% of body volume to its respiratory system [71],
mostly unidirectional airflow unlikely to permanently trap gray dust, but
~20% of the bird respiratory volume consists of tidally exchanged air in
8-9 anterior and posterior air sacs, and air spaces in the bones [71].
Assuming dead air in birds represents 38% of tidal volume as in humans
[6], and that the average bird is ~500 cm3
in volume, then the worldwide bird population has ~2 × 106
m3 of respiratory dead air which could accumulate ~1013
aerovores if the birds are breathing replibot-contaminated air at
a concentration equivalent to ~1% atmospheric opacity. In this case
~10-12 of the global aerovore population resides inside
bird respiratory systems (~40 replibots per bird at 1% opacity), necessitating
specialized quarantine or inspection and release protocols for birds passing
through the dragnet. Under similar exposure, ~7 × 1013
aerovores (~3 × 10-12 of the total) could reside in all
human lungs worldwide, or ~10,000 aerovores/person.

8.3 Gray Lichens

Colonies of symbiotic algae and fungi known as lichens (which some have
called a form of sub-aerial biofilm) are among the first plants to grow
on bare stone, helping in soil formation by slowly etching the rock [55].
Lithobiontic microbial communities such as crustose saxicolous lichens
penetrate mineral surfaces up to depths of 1 cm using a complex dissolution,
selective transport, and recrystallization process sometimes termed "biological
weathering" [56]. Colonies of epilithic (living
on rock surfaces) microscopic bacteria produce a 10 micron thick patina
on desert rocks (called "desert varnish" [57])
consisting of trace amounts of Mn and Fe oxides that help to provide protection
from heat and UV radiation [57-59].
In theory, replicating nanorobots could be made almost entirely of nondiamondoid
materials including noncarbon chemical elements found in great abundance
in rock such as silicon, aluminum, iron, titanium and oxygen (Section
2). The subsequent ecophagic destruction of land-based biology by a
maliciously programmed noncarbon epilithic replicator population that has
grown into a significant nanomass is the "gray lichen" scenario.

The growth rate of gray lichens on the surface of the Earth will be
primarily energy-limited, not materials-limited. While it is true that
chemolithotrophic microorganisms such as Thiobacillus ferrooxidans use
reduced iron and sulfur compounds for their energy source [60-62],
and that other chemolithotrophic bacteria can metabolize inorganic carbon
(e.g., assimilating CO2 from carbonate rock) using a pathway
similar to green plants [63], such energy sources
appear to be far less plentiful than ambient sunlight because most rocks
are already fully oxidized. (For example, the oxidation of Fe++
to Fe+++ by chemolithotrophs liberates only 0.75 MJ/kg [64],
as compared to ~16 MJ/kg for the combustion of glucose in oxygen [6].)
Assuming that up to 400 W/m2 in the visible spectrum is harvested
with 30% efficiency for 8 hours/day over the entire landmass of Earth,
the 6 ×1015 watts theoretically available could produce
at most ~6 ×107 kg/sec of mineral nanomass taking Ediss
~ 100 MJ/kg as before. Even assuming an optimal dispersal pattern, ~2.6
years would be required for the growing mineral nanomass to equal the terrestrial
biomass (~5 ×1015 kg; Section
3), whereupon the top ~1 cm of Earth's entire continental land area
would have been converted to nanomass.

Continuous direct census sampling of the Earth's land surfaces will
almost certainly allow early detection, since mineralogical nanorobots
should be easily distinguishable from inert rock particles and from organic
microbes in the top 3-8 cm of soil, typically 2.1 ×1013
m-3 of aerobic bacteria, 5.6
×1012 m-3
of actinomycetes, 5.2 ×1012 m-3
of anaerobic bacteria, 3.2 ×1011 m-3
fungi, and 6.7 ×1010 m-3
of algae [64].

8.4 Malicious Ecophagy

More difficult scenarios involve ecophagic attacks that are launched not
to convert biomass to nanomass, but rather primarily to destroy biomass.
The optimal malicious ecophagic attack strategy appears to involve a two-phase
process. In the first phase, initial seed replibots are widely distributed
in the vicinity of the target biomass, replicating with maximum stealth
up to some critical population size by consuming local environmental substrate
to build nanomass. In the second phase, the now-large replibot population
ceases replication and exclusively undertakes its primary destructive purpose. More generally, this strategy may be described as Build/Destroy.

During the Build phase of the malicious "badbots," and assuming technological
equivalence, defensive "goodbots" enjoy at least three important tactical
advantages over their adversaries:

Preparation -- defensive agencies can manufacture and position in advance
overwhelming quantities of (ideally, non-self-replicating) defensive instrumentalities,
e.g., goodbots, which can immediately be deployed at the first sign of
trouble, with minimal additional risk to the environment;

Efficiency -- while badbots must simultaneously replicate and defend themselves
against attack (either actively or by maintaining stealth), goodbots may
concentrate exclusively on attacking badbots (e.g., because of their large
numerical superiority in an early deployment) and thus enjoy lower operational
overhead and higher efficiency in achieving their purpose, all else equal;
and

Leverage -- in terms of materials, energy, time and sophistication, fewer
resources are generally required to confine, disable, or destroy a complex
machine than are required to build or replicate the same complex machine
from scratch (e.g., one small bomb can destroy a large bomb-making factory;
one small missile can sink a large ship).

However, once the badbots enter their Destroy phase, only the first advantage
of the defenders (i.e., preparation) remains fully effective. Of course,
a total mass Mgoodbots of
nonreplicating defensive nanorobots can hold constant a population Mbadbots
of self-replicating biovorous nanorobots if Mgoodbots(tdestroy / t)
Mbadbots,
where tdestroy is the time
required for a goodbot to find and permanently restrain, disable or destroy
a badbot (which has a replication time t);
usually, tdestroy <<
t.

Nevertheless it is most advantageous to engage a malicious ecophagic
threat while it is still in its Build phase. This requires foresight
and a commitment to extensive surveillance by the defensive authorities.
A complete analysis is beyond the scope of this paper, but two simple examples
will suffice to illustrate the level of surveillance required.

First, consider a population of Nbot
replibots that have infested a human body and are about to enter their
Destroy phase. These badbots are assumed to be motile spherical nanorobots
of radius Rnano, capable
of drilling through tissue at velocity vnano;
encountered tissue is destroyed with efficiency ke,
and a mass fraction fdest
of the biomass must be destroyed to produce death. The time required
to kill is:

where h is mean
tissue viscosity. The mass fraction of badbots that can produce death
in a time tkill is fn
= Mbadbot / Mbody,
where total badbot mass is Mbadbot
= (4/3) prnanoRnano3Nbot
and rnano
is nanorobot density. Obtaining Nbot
by solving
Eqn. 13 for Nbot,
then substituting vnano
obtained from Eqn. 12, gives:

fn = [(4 fdestrnano)
/ (kerbody)]
[h / (2 ffuelEfueletkill)]½

(14)

The number of attacking badbots is then:

Nbot = 3 fnMbody
/ (4 prnanoRnano3)

(15)

Taking fdest = 0.1 (10%),
ke
= 0.5 (50%), e
= 0.5 (50%), ffuel = 0.1
(10%), Rnano = 1 micron,
rnano
= 2000 kg/m3, h
~ 1000 kg/m-sec [6], and rbody
= Mbody / Vbody
where Mbody = 70 kg and
body volume Vbody = 0.06
m3 [6], then a kill time tkill
= 1 sec requires fn = 6
×10-4 and Nbot
= 5 ×1012 badbots. However, if the body is
monitored continuously such that a whole-body badbot dose as small as 1
mg can be detected, then fn
~ 10-8 (Nbot
~ 108 badbots) and tkill
increases dramatically to ~60 years, giving plenty of time for defense.
If the potential victim's body (comprised of Ncell
~1014 native and foreign cells [6])
contains a continuously-circulating population NbotM
of cell-monitoring nanorobots each requiring ctime
~ 100 sec/cell to enter and examine a cell for badbot intruders,
and if every cell in the body is to be checked once every day (tbody
~ 105 sec), then NbotM
= ctimeNcell
/ tbody ~ 1011
cell-monitors, with total fleet volume ~ 0.1 cm3 assuming Rnano
= 1 micron. At fn
~ 10-8, a badbot resides, on average, in one of every 106
cells, assuming uniform distribution. The hypothesized monitoring
system examines ~106 cells every 0.001 sec, so a badbot infection
of this magnitude is first detected in ~1 millisec, allowing a massive
and immediate "immune" response.

Second, consider the defense of the entire eukaryotic biosphere. Excluding
bacteria assumed to represent about half of global biomass and assuming
an average eukaryotic cell size of 20 microns, there are ~3 ×1026
eukaryotic cells on Earth. If each cell is visited and examined,
on average, about once a year with time spent per cell ctime
= 100 sec/cell as before, this implies a global examination rate of Xcell
~ 1019 cells/sec and a requirement for Xcellctime
~ 1021 cell-monitoring nanorobots, representing a total
worldwide nanomachine volume of ~1000 m3 of 1-micron nanorobots
consuming ~10 GW (~0.1% total current human global power generation) assuming
~10 pW/device. In this surveillance regime, a ~1 mg infestation of
1-micron badbots in a 3 meter wide, 30 meter tall redwood tree (fn
~ 10-11) is first detected in ~100 millisec -- again,
triggering a prompt corrective response.

9.0 Conclusions
and Public Policy Recommendations

The smallest plausible biovorous nanoreplicator has a molecular weight
of ~1 gigadalton and a minimum replication time of perhaps ~100 seconds,
in theory permitting global ecophagy to be completed in as few as ~104
seconds. However, such rapid replication creates an immediately detectable
thermal signature enabling effective defensive policing instrumentalities
to be promptly deployed before significant damage to the ecology can occur.
Such defensive instrumentalities will generate their own thermal pollution
during defensive operations. This should not significantly limit the defense
strategy because knapsacking, disabling or destroying a working nanoreplicator
should consume far less energy than is consumed by a nanoreplicator during
a single replication cycle, hence such defensive operations are effectively
endothermic.

Ecophagy that proceeds near the current threshold for immediate climatological
detection, adding perhaps ~4°C to global warming, may require ~20 months
to run to completion, which is plenty of advance warning to mount an effective
defense.

Ecophagy that progresses slowly enough to evade easy detection by thermal
monitoring alone would require many years to run to completion, could still
be detected by direct in situ surveillance, and may be at least partially
offset by increased biomass growth rates due to natural homeostatic compensation
mechanisms inherent in the terrestrial ecology.

Ecophagy accomplished indirectly by a replibot population pre-grown
on nonbiological substrate may be avoided by diligent thermal monitoring
and direct census sampling of relevant terrestrial niches to search for
growing, possibly dangerous, pre-ecophagous nanorobot populations.

Specific public policy recommendations suggested by the results of the
present analysis include:

an immediate international moratorium on all artificial life experiments
implemented as nonbiological hardware. In this context, "artificial life"
is defined as autonomous foraging replicators, excluding purely biological
implementations (already covered by NIH guidelines [65]
tacitly accepted worldwide) and also excluding software simulations which
are essential preparatory work and should continue. Alternative "inherently
safe" replication strategies such as the broadcast architecture [66]
are already well-known.

continuous comprehensive infrared surveillance of Earth's surface by geostationary
satellites, both to monitor the current biomass inventory and to detect
(and then investigate) any rapidly-developing artificial hotspots. This
could be an extension of current or proposed Earth-monitoring systems (e.g.,
NASA's Earth Observing System [67]and disease remote-sensing
programs [93]) originally intended to understand
and predict global warming, changes in land use, and so forth -- initially
using non-nanoscale technologies. Other methods of detection are feasible
and further research is required to identify and properly evaluate the
full range of alternatives.

initiating a long-term research program designed to acquire the knowledge
and capability needed to counteract ecophagic replicators, including scenario-building
and threat analysis with numerical simulations, measure/countermeasure
analysis, theory and design of global monitoring systems capable of fast
detection and response, IFF (Identification Friend or Foe) discrimination
protocols, and eventually the design of relevant nanorobotic systemic defensive
capabilities and infrastructure. A related long-term recommendation
is to initiate a global system of comprehensive in situ ecosphere surveillance,
potentially including possible nanorobot activity signatures (e.g. changes
in greenhouse gas concentrations), multispectral surface imaging to detect
disguised signatures, and direct local nanorobot census sampling on land,
sea, and air, as warranted by the pace of development of new MNT capabilities.

U.S. Bureau of the Census, Statistical
Abstract of the United States: 1996, 116th Edition, Washington, DC, October
1996.

"...there are dozens of HIV-like
viruses in wild monkey populations, and if natural transfer of AIDS viruses
from chimpanzees to monkeys has already occurred, there is no reason why
it should not happen again." Beatrice Hahn, Howard Hughes Medical Institute
scientist, quoted in: Declan Butler, "Analysis of polio vaccine could end
dispute over how AIDS originated," Nature404(2 March 2000):9.